In this unit, “What’s My Angle”, students will explore and identify angles in our world and create a digital story that shares their favorite angles in our environment. After learning to name, estimate, and measure angles with a protractor, students will create a video in groups that explain the proper steps to measure an angle. Next, students will create and name a geometric character using lines, angles, and circles to use in their final unit project. Student will classify pairs of angles as complementary or supplementary and draw the complement or supplement of a given angle using Google Drawing. Last, as a final unit project, students will choose one of three products to create: · Web 2.0 tool illustrating geometry vocabulary · Math dictionary with geometry vocabulary learned during the unit · Geometric Art Design or poster using lines, points, and angles
Lesson Description for Days 7- 9
Pre-Requisites to lesson:
· Identify and name angles: right, acute, obtuse, reflex · Estimate, measure, and draw angles · Vocabulary: vertex, ray, line, line segment, parallel, perpendicular, degree
State/post learning goals for lesson:
· Students will identify pairs of angles as complementary or supplementary · Student will identify, measure, and draw congruent angles · Students will identify, solve, measure, and draw the complement or supplement of a given angle. · Students will identify adjacent angles · Students will use formula in spreadsheet · Students will use drawing tools
Students will sort careers on a T-chart as they brainstorm which ones use the measurement of angles and which ones do not. Students will explore a website that shows the many different careers that are impacted by angles and explore the salaries of each career. Students will then watch several videos as they learn about supplementary and complementary angles. In groups, students will set up a formula in Google spreadsheet to calculate the supplement and complement of a drawn angle. Students will practice estimating, measuring, and solving for the supplement and complement of a given angle. Students will collaborate, plan, and create a geometric character according to a list of criteria to include. During the entire unit, students will have access to the class wiki that will have unit activities, vocabulary, reflections, KWHL charts, templates, documents, rubrics and links.
State Standards:
Mathematics, Grade 6
Standard 6: Geometry and spatial reasoning. The student uses geometric vocabulary to describe angles, polygons, and circles. The student is expected to: (A) use angle measurements to classify angles as acute, obtuse, or right;
Standard 8: Measurement. The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles. The student is expected to: (A) estimate measurements and evaluate reasonableness of results; (B) select and use appropriate units, tools, or formulas to measure and to solve problems involving length, area, time, temperature, volume, and weight; (C) measure angles;
Standard 11: Underlying processes and mathematical tools. The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.
Standard 12: Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models. The student is expected to: (A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models;
Standard 13: Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: (B) validate his/her conclusions using mathematical properties and relationships.
Mathematics, Grade 7
Standard 6: Geometry and spatial reasoning. The student compares and classifies two- and three- dimensional figures using geometric vocabulary and properties. The student is expected to: (A) use angle measurements to classify pairs of angles as complementary or supplementary;
Standard 13: Underlying processes and mathematical tools. The student applies Grade 7 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to: (A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics; (B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; (C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and (D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.
Standard 14: Underlying processes and mathematical tools. The student communicates about Grade 7 mathematics through informal and mathematical language, representations, and models. The student is expected to: (A) communicate mathematical ideas using language, efficient tools, Appropriate units, and graphical, numerical, physical, or algebraic mathematical models; and (B) evaluate the effectiveness of different representations to communicate ideas.
Standard 15: Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to: (A) make conjectures from patterns or sets of examples and nonexamples; and (B) validate his/her conclusions using mathematical properties and relationships.
Technology Standards, Grades 6-8
NETS:
1. Creativity and Innovation Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology. Students:
a. apply existing knowledge to generate new ideas, products, or processes b. create original works as a means of personal or group expression c. use models and simulations to explore complex systems and issues
2. Communication and Collaboration Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others. Students:
a. interact, collaborate, and publish with peers, experts, or others employing a variety of digital environments and media b. communicate information and ideas effectively to multiple audiences using a variety of media and formats d. contribute to project teams to produce original works or solve problems
4. Critical Thinking, Problem Solving, and Decision Making Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources. Students:
a. identify and define authentic problems and significant questions for investigation b. plan and manage activities to develop a solution or complete a project c. collect and analyze data to identify solutions and/or make informed decisions d. use multiple processes and diverse perspectives to explore alternative solutions
5. Digital Citizenship Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior. Students:
a. advocate and practice safe, legal, and responsible use of information and technology b. exhibit a positive attitude toward using technology that supports collaboration, learning, and productivity c. demonstrate personal responsibility for lifelong learning d. exhibit leadership for digital citizenship
6. Technology Operations and Concepts Students demonstrate a sound understanding of technology concepts, systems, and operations. Students:
a. understand and use technology systems b. select and use applications effectively and productively c. troubleshoot systems and applications d. transfer current knowledge to learning of new technologies
Goals
Unit Goals:
· Students will be able to describe right, acute, & obtuse angles · Students will be able to locate right, acute, & obtuse angles in the real world · Students will estimate the measurement of an angle · Students will analyze and measure an angle using a protractor · Students will identify pairs of lines as complementary or supplementary · Students will identify and draw the complement or supplement of a given angle
Lesson Goals:
· Students will discover careers that use geometric angles · Students will identify pairs of angles as complementary or supplementary · Students will solve for the complement or supplement of a given angle · Students will draw the complement or supplement of a given angle · Students will use drawing tools and formula in spreadsheet
Methods
Anticipatory Set:
(Recognition Network)
Day 7: Time: 20 min. · Students will take a Pre-Self-Evaluation before the lessons to evaluate their previous learning. · Vocabulary Review: Flashcards, matching, concentration, and word search at this link:http://www.quia.com/jg/318570.html
Day 8: Time: 10 min. · Display the website and eBook we will use to show the four basic concepts on which Geometry is built upon: http://www.math.com/school/subject3/lessons/S3U1L1GL.html · Review the concepts focusing on the various dimensions: 2-D, 3-D, and none. (Stop on Step 1)
Day 9: Time: 10 min. · Using the interactive visuals for complementary and supplementary angles (link given) have students solve for the complement and/or supplement as teacher covers the answer and gives immediate feedback by uncovering answer.
· Students will fill out their Learning Goal Contract (template)
Have students think about geometric angles and its impact in the workforce? Share the T-chart and explain activity for students
· Divide students into groups to complete T-chart with given careers. Students will categorize careers by sorting them into ones that use geometric angles vs. careers that do not use geometric angles · Class discussion…review ideas having students justify and give reasons why they placed it under the chosen category
Recall Day 7’s discovery of the impact of geometric angles in careers. Share an object we use daily to teach angles (clocks)
· **BrainPOP video on Angles**- stop and point out the new vocabulary of supplementary and complementary angles (Ask if these type of angles are two-dimensional or three-dimensional) · Using your IWB model how to draw congruent angles using a protractor (share the symbol for congruent) · Using your IWB introduce supplementary and complementary angles or show these two videos from Teacher.com
Complementary angles: Teacher.com’s YouTube http://www.youtube.com/watch?feature=player_detailpage&v=93gal5blsU4 (teacher needs to have video ready by passing the advertisements and having it set on the beginning of video) Supplementary angles: Teacher.com’s YouTube http://www.youtube.com/watch?v=3gwcv9LSBO8&feature=fvwrel (teacher needs to have video ready by passing the advertisements and having it set on the beginning of video) · Using your IWB model how to solve for the complement or supplement of a given angle. Model several examples for students, and review how to draw it using your protractor. Ask for questions and if students need more clarification. Day 9: Time: 15 min.
Activity – Part 2 Students will continue to work with same group, partner, or independently on their Google spreadsheet. Teacher will facilitate and provide help as necessary. Teacher will share the Drawing tools in Google and share how to add this to their spreadsheet. Teacher will show the speech bubble and how to manipulate it to the character’s mouth. Students will work to create their geometric characters for their spreadsheet.
· Students will create and name a geometric character that includes the following geometric criteria: parallel line, perpendicular line, acute angle, obtuse angle, right angle, circle, point, ray, line, half circle, straight angle and adjacent angles. The character will be saved as a jpeg to be used in the final Unit project. Students can choose to do this in any paint program, PowerPoint slide, Microsoft Word, Google Doc, etc. · Insert a speech bubble with text that includes character’s name. Make sure that all lines and angles can be identified by each group member.
Review the four basic geometry concepts in the Ebook
Day 8: Time: 20 min.
Activity (Part 1) Teacher will model using Google Spreadsheet for this activity (Part 1) before going into the lab. Students will choose to work in partners, groups, or independently complete the activity on Google spreadsheet. Students will complete the following items on their spreadsheet:
· Minus formula for Complementary angles (pull down to include at least 5 different data inputs) · Minus formula for Supplementary angles (pull down to include at least 5 different data inputs) · Draw the following by using Google’s (Insert) Drawing menu and selecting line tool: right angle, acute angle, obtuse angle, straight angle · Label each angle with the name and correct measurement · Enter those measurements in formulas to calculate the complement or supplement angles and draw those angles (with labels also)
What will you have to know to complete this activity? How will you know if you need to find the complement or supplement of the angle that was drawn? How will you know if the angles are Supplementary? How will you know if the angles are Complementary?
Day 9: Time: 35 min. Students continue work on project according to their choice (independent, partner, or group) and complete Part 2 of the activity: adding the Geometric character to the spreadsheet with speech bubble.
Provide Independent Practice:
Students will have access to many online learning resources through the class wiki. Students are given link on the teacher’s website to use at any time Wiki: **“What’s My Angle?”**
Day 8 Homework: Watch video on supplementary and complementary angles: http://www.youtube.com/watch?v=tPjJ4DI2yO8 Choose one of the activities to do that are available on our BrainPOP movie: Word Find, Vocabulary, or graphic organizer
Teacher will use the data from the Pre-Self-Assessment and the learning contracts to evaluate students’ prior knowledge and new learning desired. Teacher will monitor and guide learning during lesson activities. Questions and answers will be provided to direct and clarify problems during teacher observations. Students’ reflections will be assessed daily and comments will be added to support students throughout the unit. Evaluation of student products on spreadsheet and monitoring the learning will be given as students work collaboratively to complete the project. Online quizzes are assigned throughout the lessons with immediate feedback and used for review.
Summative/End of Lesson Assessment:
Evaluation of student product will be assessed by rubric. Teacher will give the Post-Self-Assessment to evaluate students’ learning. Student reflections on the overall unit will be assessed to make changes to unit if necessary.
An end of unit quiz will be given after students’ final project is completed.
Accomodations
Gifted and Talented: online resources; choice of work; independent enrichment activities; rubrics; self-assessments; interactive games with immediate feedback; group work.
Disabled: group work; instructor aide; eBook; online resources; modified lessons; hands-on activities where applicable.
Blind: hands-on activities where applicable; eBook; podcasts of lessons; audio flashcards; braille tools; group activities; instructor aide; text-to-speech software.
Deaf: instructor aide that can sign; group work; eBook; videos with closed captions; visuals and online activities; audio trainer; printed instructions for lessons.
Multiple achievement levels: choice in activities to take in interests; levels of difficulty on online activities; group work; peer-teaching; differentiated activities; enrichment activities.
Lesson Overview
· Web 2.0 tool illustrating geometry vocabulary
· Math dictionary with geometry vocabulary learned during the unit
· Geometric Art Design or poster using lines, points, and angles
· Identify and name angles: right, acute, obtuse, reflex
· Estimate, measure, and draw angles
· Vocabulary: vertex, ray, line, line segment, parallel, perpendicular, degree
State/post learning goals for lesson:
· Students will identify pairs of angles as complementary or supplementary
· Student will identify, measure, and draw congruent angles
· Students will identify, solve, measure, and draw the complement or supplement of a given angle.
· Students will identify adjacent angles
· Students will use formula in spreadsheet
· Students will use drawing tools
Students will sort careers on a T-chart as they brainstorm which ones use the measurement of angles and which ones do not. Students will explore a website that shows the many different careers that are impacted by angles and explore the salaries of each career. Students will then watch several videos as they learn about supplementary and complementary angles. In groups, students will set up a formula in Google spreadsheet to calculate the supplement and complement of a drawn angle. Students will practice estimating, measuring, and solving for the supplement and complement of a given angle. Students will collaborate, plan, and create a geometric character according to a list of criteria to include. During the entire unit, students will have access to the class wiki that will have unit activities, vocabulary, reflections, KWHL charts, templates, documents, rubrics and links.
Standard 6: Geometry and spatial reasoning.
The student uses geometric vocabulary to describe angles, polygons, and circles. The student is expected to:
(A) use angle measurements to classify angles as acute,
obtuse, or right;
Standard 8: Measurement.
The student solves application problems involving estimation and measurement of length, area, time, temperature, volume, weight, and angles. The student is expected to:
(A) estimate measurements and evaluate reasonableness of results;
(B) select and use appropriate units, tools, or formulas to measure and to solve problems involving length, area, time, temperature, volume, and weight;
(C) measure angles;
Standard 11: Underlying processes and mathematical tools.
The student applies Grade 6 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:
(D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.
Standard 12: Underlying processes and mathematical tools. The student communicates about Grade 6 mathematics through informal and mathematical language, representations, and models. The student is expected to:
(A) communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models;
Standard 13: Underlying processes and mathematical tools. The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to:
(B) validate his/her conclusions using mathematical properties and relationships.
Mathematics, Grade 7
Standard 6: Geometry and spatial reasoning. The student compares and classifies two- and three- dimensional figures using geometric vocabulary and properties. The student is expected to:
(A) use angle measurements to classify pairs of angles as complementary or supplementary;
Standard 13: Underlying processes and mathematical tools. The student applies Grade 7 mathematics to solve problems connected to everyday experiences, investigations in other disciplines, and activities in and outside of school. The student is expected to:
(A) identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;
(B) use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness;
(C) select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; and
(D) select tools such as real objects, manipulatives, paper/pencil, and technology or techniques such as mental math, estimation, and number sense to solve problems.
Standard 14: Underlying processes and mathematical tools. The student communicates about Grade 7 mathematics through informal and mathematical language, representations, and models. The student is expected to:
(A) communicate mathematical ideas using language, efficient tools,
Appropriate units, and graphical, numerical, physical, or algebraic mathematical models; and
(B) evaluate the effectiveness of different representations to communicate ideas.
Standard 15: Underlying processes and mathematical tools.
The student uses logical reasoning to make conjectures and verify conclusions. The student is expected to:
(A) make conjectures from patterns or sets of examples and nonexamples; and
(B) validate his/her conclusions using mathematical properties and relationships.
Technology Standards, Grades 6-8
NETS:
1. Creativity and Innovation
Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology. Students:
a. apply existing knowledge to generate new ideas, products, or processes
b. create original works as a means of personal or group expression
c. use models and simulations to explore complex systems and issues
2. Communication and Collaboration
Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others. Students:
a. interact, collaborate, and publish with peers, experts, or others employing a variety of digital environments
and media
b. communicate information and ideas effectively to multiple audiences using a variety of media and formats
d. contribute to project teams to produce original works or solve problems
4. Critical Thinking, Problem Solving, and Decision Making
Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources. Students:
a. identify and define authentic problems and significant questions for investigation
b. plan and manage activities to develop a solution or complete a project
c. collect and analyze data to identify solutions and/or make informed decisions
d. use multiple processes and diverse perspectives to explore alternative solutions
5. Digital Citizenship
Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior. Students:
a. advocate and practice safe, legal, and responsible use of information and technology
b. exhibit a positive attitude toward using technology that supports collaboration, learning, and productivity
c. demonstrate personal responsibility for lifelong learning
d. exhibit leadership for digital citizenship
6. Technology Operations and Concepts
Students demonstrate a sound understanding of technology concepts, systems, and operations. Students:
a. understand and use technology systems
b. select and use applications effectively and productively
c. troubleshoot systems and applications
d. transfer current knowledge to learning of new technologies
Goals
· Students will be able to locate right, acute, & obtuse angles in the real world
· Students will estimate the measurement of an angle
· Students will analyze and measure an angle using a protractor
· Students will identify pairs of lines as complementary or supplementary
· Students will identify and draw the complement or supplement of a given angle
· Students will identify pairs of angles as complementary or supplementary
· Students will solve for the complement or supplement of a given angle
· Students will draw the complement or supplement of a given angle
· Students will use drawing tools and formula in spreadsheet
Methods
Day 7: Time: 20 min.
· Students will take a Pre-Self-Evaluation before the lessons to evaluate their previous learning.
· Vocabulary Review: Flashcards, matching, concentration, and word search at this link:http://www.quia.com/jg/318570.html
Day 8: Time: 10 min.
· Display the website and eBook we will use to show the four basic concepts on which Geometry is built upon:
http://www.math.com/school/subject3/lessons/S3U1L1GL.html
· Review the concepts focusing on the various dimensions: 2-D, 3-D, and none. (Stop on Step 1)
Day 9: Time: 10 min.
· Using the interactive visuals for complementary and supplementary angles (link given) have students solve for the complement and/or supplement as teacher covers the answer and gives immediate feedback by uncovering answer.
Finding the complement:
http://www.mathopenref.com/anglecomplementary.html
Finding the supplement:
http://www.mathopenref.com/anglesupplementary.html
Day 7: Time: 20 min.
· Students will fill out their Learning Goal Contract (template)
Have students think about geometric angles and its impact in the workforce? Share the T-chart and explain activity for students
· Divide students into groups to complete T-chart with given careers. Students will categorize careers by sorting them into ones that use geometric angles vs. careers that do not use geometric angles
· Class discussion…review ideas having students justify and give reasons why they placed it under the chosen category
Share link: XP Math: Math in Careers Database Introduce website and its features then have students explore in their group
Day 8: Time: 25 min.
Recall Day 7’s discovery of the impact of geometric angles in careers. Share an object we use daily to teach angles (clocks)
· **BrainPOP video on Angles**- stop and point out the new vocabulary of supplementary and complementary angles (Ask if these type of angles are two-dimensional or three-dimensional)
· Using your IWB model how to draw congruent angles using a protractor (share the symbol for congruent)
· Using your IWB introduce supplementary and complementary angles or show these two videos from Teacher.com
Complementary angles: Teacher.com’s YouTube http://www.youtube.com/watch?feature=player_detailpage&v=93gal5blsU4
(teacher needs to have video ready by passing the advertisements and having it set on the beginning of video)
Supplementary angles: Teacher.com’s YouTube http://www.youtube.com/watch?v=3gwcv9LSBO8&feature=fvwrel
(teacher needs to have video ready by passing the advertisements and having it set on the beginning of video)
· Using your IWB model how to solve for the complement or supplement of a given angle. Model several examples for students, and review how to draw it using your protractor.
Ask for questions and if students need more clarification.
Day 9: Time: 15 min.
Activity – Part 2
Students will continue to work with same group, partner, or independently on their Google spreadsheet. Teacher will facilitate and provide help as necessary. Teacher will share the Drawing tools in Google and share how to add this to their spreadsheet. Teacher will show the speech bubble and how to manipulate it to the character’s mouth. Students will work to create their geometric characters for their spreadsheet.
· Students will create and name a geometric character that includes the following geometric criteria: parallel line, perpendicular line, acute angle, obtuse angle, right angle, circle, point, ray, line, half circle, straight angle and adjacent angles. The character will be saved as a jpeg to be used in the final Unit project. Students can choose to do this in any paint program, PowerPoint slide, Microsoft Word, Google Doc, etc.
· Insert a speech bubble with text that includes character’s name. Make sure that all lines and angles can be identified by each group member.
Day 7: Time: 20 min.
Explore website on Math careers in groups:
XP Math: Math in Careers Database
Review the four basic geometry concepts in the Ebook
Day 8: Time: 20 min.
Activity (Part 1)
Teacher will model using Google Spreadsheet for this activity (Part 1) before going into the lab. Students will choose to work in partners, groups, or independently complete the activity on Google spreadsheet. Students will complete the following items on their spreadsheet:
· Minus formula for Complementary angles (pull down to include at least 5 different data inputs)
· Minus formula for Supplementary angles (pull down to include at least 5 different data inputs)
· Draw the following by using Google’s (Insert) Drawing menu and selecting line tool: right angle, acute angle, obtuse angle, straight angle
· Label each angle with the name and correct measurement
· Enter those measurements in formulas to calculate the complement or supplement angles and draw those angles (with labels also)
What will you have to know to complete this activity? How will you know if you need to find the complement or supplement of the angle that was drawn? How will you know if the angles are Supplementary? How will you know if the angles are Complementary?
Day 9: Time: 35 min.
Students continue work on project according to their choice (independent, partner, or group) and complete Part 2 of the activity: adding the Geometric character to the spreadsheet with speech bubble.
Wiki: **“What’s My Angle?”**
Day 7 Homework: Review angles and measurement with protractor by visiting this site: http://www.amblesideprimary.com/ambleweb/mentalmaths/protractor.html
Day 8 Homework: Watch video on supplementary and complementary angles: http://www.youtube.com/watch?v=tPjJ4DI2yO8
Choose one of the activities to do that are available on our BrainPOP movie: Word Find, Vocabulary, or graphic organizer
Day 9 Homework: Multimedia tutorial for reviewing lesson:
**//http://math123xyz.com/Nav/Geometry/Angles.php//**
Interactive game to practice drawing, estimating, and measuring angles:
http://www.crickweb.co.uk/ks2numeracy-shape-and-weight.html#vpinboard4z
Assessment
Ongoing Assessment:
An end of unit quiz will be given after students’ final project is completed.
Disabled: group work; instructor aide; eBook; online resources; modified lessons; hands-on activities where applicable.
Blind: hands-on activities where applicable; eBook; podcasts of lessons; audio flashcards; braille tools; group activities; instructor aide; text-to-speech software.
Deaf: instructor aide that can sign; group work; eBook; videos with closed captions; visuals and online activities; audio trainer; printed instructions for lessons.
Multiple achievement levels: choice in activities to take in interests; levels of difficulty on online activities; group work; peer-teaching; differentiated activities; enrichment activities.
Materials